A bus starts with 9 people, two of whom are Jack and Mike, and stops at 14 locations. Assuming nobody else gets on the bus, how many ways are there...
a) for people to get off the bus?
b) for people to get off the bus if no 2 people get off at the same stop?
c) for people to get off the bus if Jack and Mike get off together?
My thinking for a) was that since there are 9 people, there are 10 possibilities at each stop (1-9 people get off or no one gets off) and this happens 14 times, so I got 10^14 via the counting principle. I'm not sure if that makes sense, though...
For b) I figured you were removing one possibility each time, so 9^14, and same for c).